Understanding room-temperature dislocation-based plastic deformation, in general, and time dependent deformation, in particular, in brittle solids is nontrivial. Herein, we describe a new constant-stress, spherical nanoindentation technique to study the creep of A-plane (1120) ZnO single crystal. The time dependent deformation follows a power-law behavior, with a threshold stress, and a stress exponent of ≈3.1±0.3, attributed to the movement of dislocation pileups on basal planes. The results are used to estimate the time dependencies of the threshold stresses, number of pileup dislocations, and the distance between them. The method described herein can also be used to quantify other time dependent mechanical properties, such as fatigue and subcritical crack growth, at the submicron, and even nanoscale. The results can then—as done here—be compared to long established macroscale relationships thus elucidating the nature of the former.